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3 Optimal Consumption with Financial Wealth Now suppose the household lives for N periods, from Period 1 to N. Household receives an exogenous income stream {y1,y2, ...yN }, and accumulate their financial wealth at in each period. The return on real financial wealth is r. Let household's problem be max E gt-1In(ct) (1) ct t= 1 subject to at+1 = (1 + r)at + yt - ct (2) Ct 2 0 (3) aN+1 20 (4) where at is the financial wealth at the beginning of Period t and a1 = 0. 1. Interpret (1)(2) (3) and (4). 2. Write down the inter-temporal budget constraint and derive the Euler equation(s). 3. Assume B = 1, r = 0. Solve for the optimal consumption for each period, {cf }, t = 1, 2, ..., N. Explain how your results are related to permanent income theory